Asymptotic normality of in- and out-degree counts in a preferential attachment model

Preferential attachment in a directed scale-free graph is an often used paradigm for modeling the evolution of social networks. Social network data is usually given in a format allowing recovery of the number of nodes with in-degree i and out-degree j. Assuming a model with preferential attachment, formal statistical procedures for estimation can be based on such data summaries. Anticipating the statistical need for such node-based methods, we prove asymptotic normality of the node counts. Our approach is based on a martingale construction and a martingale central limit theorem.     

Frailty effects in networks: comparison and identification of individual heterogeneity versus preferential attachment in evolving networks

Preferential attachment is a proportionate growth process in networks, where nodes receive new links in proportion to their current degree. Preferential attachment is a popular generative mechanism to explain the widespread observation of power-law-distributed networks. An alternative explanation for the phenomenon is a randomly grown network with large individual variation in growth rates among the nodes (frailty). We derive analytically the distribution of individual rates, which will reproduce the connectivity distribution that is obtained from a general preferential attachment process (Yule process), and the structural differences between the two types of graphs are examined by simulations. We present a statistical test to distinguish the two generative mechanisms from each other and we apply the test to both simulated data and two real data sets of scientific citation and sexual partner networks. The findings from the latter analyses argue for frailty effects as an important mechanism underlying the dynamics of complex networks.     

ESTIMATING WITHIN-SCHOOL CONTACT NETWORKS TO UNDERSTAND INFLUENZA TRANSMISSION

Many epidemic models approximate social contact behavior by assuming random mixing within mixing groups (e.g., homes, schools, and workplaces). The effect of more realistic social network structure on estimates of epidemic parameters is an open area of exploration. We develop a detailed statistical model to estimate the social contact network within a high school using friendship network data and a survey of contact behavior. Our contact network model includes classroom structure, longer durations of contacts to friends than non-friends and more frequent contacts with friends, based on reports in the contact survey. We performed simulation studies to explore which network structures are relevant to influenza transmission. These studies yield two key findings. First, we found that the friendship network structure important to the transmission process can be adequately represented by a dyad-independent exponential random graph model (ERGM). This means that individual-level sampled data is sufficient to characterize the entire friendship network. Second, we found that contact behavior was adequately represented by a static rather than dynamic contact network. We then compare a targeted antiviral prophylaxis intervention strategy and a grade closure intervention strategy under random mixing and network-based mixing. We find that random mixing overestimates the effect of targeted antiviral prophylaxis on the probability of an epidemic when the probability of transmission in 10 minutes of contact is less than 0.004 and underestimates it when this transmission probability is greater than 0.004. We found the same pattern for the final size of an epidemic, with a threshold transmission probability of 0.005. We also find random mixing overestimates the effect of a grade closure intervention on the probability of an epidemic and final size for all transmission probabilities. Our findings have implications for policy recommendations based on models assuming random mixing, and can inform further development of network-based models.     

Estimating Spatial Autocorrelation With Sampled Network Data

Spatial autocorrelation is a parameter of importance for network data analysis. To estimate spatial autocorrelation, maximum likelihood has been popularly used. However, its rigorous implementation requires the whole network to be observed. This is practically infeasible if network size is huge (e.g., Facebook, Twitter, Weibo, WeChat, etc.). In that case, one has to rely on sampled network data to infer about spatial autocorrelation. By doing so, network relationships (i.e., edges) involving unsampled nodes are overlooked. This leads to distorted network structure and underestimated spatial autocorrelation. To solve the problem, we propose here a novel solution. By temporarily assuming that the spatial autocorrelation is small, we are able to approximate the likelihood function by its first-order Taylor’s expansion. This leads to the method of approximate maximum likelihood estimator (AMLE), which further inspires the development of paired maximum likelihood estimator (PMLE). Compared with AMLE, PMLE is computationally superior and thus is particularly useful for large-scale network data analysis. Under appropriate regularity conditions (without assuming a small spatial autocorrelation), we show theoretically that PMLE is consistent and asymptotically normal. Numerical studies based on both simulated and real datasets are presented for illustration purpose.     

城市网络位置与疫情风险

作为重大突发公共卫生事件,传染病疫情风险是一个值得关注的前沿新论题。本文从一个较新的网络拓扑视角,以新冠肺炎疫情为例,构建了一个由病毒感染人群流动形成的城市间疫情关联网络,并探讨了城市在疫情关联网络中的位置对其疫情风险的影响。研究发现,城市之间的传染病疫情呈现出紧密的网络关联性;疫情的风险程度与城市在疫情关联网络中的位置密切相关,处在网络重要位置的城市与其他城市关联度较高,从而面临更大的疫情风险,这一点在针对城市群和交通枢纽聚集性感染风险研究中尤为突出。拓展分析表明,城市网络中心度具有疫情扩散风险放大效应,关闭离汉通道措施有助于降低城市在疫情关联网络中的核心位置对本城市疫情风险的影响。     

Estimating time-varying directed neural networks

Reconstructing the functional network of a neuron cluster is a fundamental step to reveal the complex interactions among neural systems of the brain. Current approaches to reconstruct a network of neurons or neural systems focus on establishing a static network by assuming the neural network structure does not change over time. To the best of our knowledge, this is the first attempt to build a time-varying directed network of neurons by using an ordinary differential equation model, which allows us to describe the underlying dynamical mechanism of network connections. The proposed method is demonstrated by estimating a network of wide dynamic range neurons located in the dorsal horn of the rats’ spinal cord in response to pain stimuli applied to the Zusanli acupoint on the right leg. The finite sample performance of the proposed method is also investigated with a simulation study.

     

Fast Inference for Network Models of Infectious Disease Spread

Models of infectious disease over contact networks offer a versatile means of capturing heterogeneity in populations during an epidemic. Highly connected individuals tend to be infected at a higher rate early during an outbreak than those with fewer connections. A powerful approach based on the probability generating function of the individual degree distribution exists for modelling the mean field dynamics of outbreaks in such a population. We develop the same idea in a stochastic context, by proposing a comprehensive model for 1‐week‐ahead incidence counts. Our focus is inferring contact network (and other epidemic) parameters for some common degree distributions, in the case when the network is non‐homogeneous ‘at random’. Our model is initially set within a susceptible–infectious–removed framework, then extended to the susceptible–infectious–removed–susceptible scenario, and we apply this methodology to influenza A data.     

Bayesian Inference for Contact Networks Given Epidemic Data

Abstract. In this article, we estimate the parameters of a simple random network and a stochastic epidemic on that network using data consisting of recovery times of infected hosts. The SEIR epidemic model we fit has exponentially distributed transmission times with Gamma distributed exposed and infectious periods on a network where every edge exists with the same probability, independent of other edges. We employ a Bayesian framework and Markov chain Monte Carlo (MCMC) integration to make estimates of the joint posterior distribution of the model parameters. We discuss the accuracy of the parameter estimates under various prior assumptions and show that it is possible in many scientifically interesting cases to accurately recover the parameters. We demonstrate our approach by studying a measles outbreak in Hagelloch, Germany, in 1861 consisting of 188 affected individuals. We provide an R package to carry out these analyses, which is available publicly on the Comprehensive R Archive Network.     

A network analysis of student mobility patterns from high school to master’s

Human migration involves the movement of people from one place to another. An example of undirected migration is Italian student mobility where students move from the South to the Center-North. This kind of mobility has become of general interest, and this work explores student mobility from Sicily towards universities outside the island. The data used in this paper regards six cohorts of students, from 2008/09 to 2013/14. In particular, our goal is to study the 3-step migration path: the area of origin (Sicilian provinces), the regional university for the bachelor’s degree, and the regional university for the master’s. Our analysis is conducted by building a multipartite network with four sets of nodes: students; Sicilian provinces; bachelor region of studies; and the master region of studies. By projecting the students’ set onto the others, we obtain a tripartite network where the number of students represents the link weight. Results show that the big Sicilian cities—Palermo, Catania, and Messina—have different preferential paths compared to small Sicilian cities. Furthermore, the results reveal preferential paths of 3-step mobility that only, in part, reflect a south-north orientation in the transition from the region of study for the bachelor degree to that for the master’s.

     

Estimation in multitype epidemics

A multitype epidemic model is analysed assuming proportionate mixing between types. Estimation procedures for the susceptibilities and infectivities are derived for three sets of data: complete data, meaning that the whole epidemic process is observed continuously; the removal processes are observed continuously; only the final state is observed. Under the assumption of a major outbreak in a population of size n it is shown that, for all three data sets, the susceptibility estimators are always efficient, i.e. consistent with a √ n rate of convergence. The infectivity estimators are 'in most cases' respectively efficient, efficient and unidentifiable. However, if some susceptibilities are equal then the corresponding infectivity estimators are respectively barely consistent (√log( n ) rate of convergence), not consistent and unidentifiable. The estimators are applied to simulated data.     

Analyzing center specific outcomes in hematopoietic cell transplantation

Reporting transplant center-specific survival rates after hematopoietic cell transplantation is required in the United States. We describe a method to report 1-year survival outcomes by center, as well as to quantify center performance relative to the transplant center network average, which can be reliably used with censored data and for small center sizes. Each center's observed 1-year survival outcome is compared to a predicted survival outcome adjusted for patient characteristics using a pseudovalue regression technique. A 95% prediction interval for 1-year survival assuming no center effect is computed for each center by bootstrapping the scaled residuals from the regression model, and the observed 1-year survival is compared to this prediction interval to determine center performance. We illustrate the technique using a recent center specific analysis performed by the Center for International Blood and Marrow Transplant Research, and study the performance of this method using simulation.     

A Partial Likelihood Estimator of Vaccine Efficacy

A partial likelihood method is proposed for estimating vaccine efficacy for a general epidemic model. In contrast to the maximum likelihood estimator (MLE) which requires complete observation of the epidemic, the suggested method only requires information on the sequence in which individuals are infected and not the exact infection times. A simulation study shows that the method performs almost as well as the MLE. The method is applied to data on the infectious disease mumps.     

The Relative Fit measure for evaluating a blockmodel

Statistical Methods & Applications - A blockmodel is a network in which the nodes are clusters of equivalent (in terms of the structure of the links connecting) nodes in the network being...     

A statistical social network model for consumption data in trophic food webs

We adapt existing statistical modeling techniques for social networks to study consumption data observed in trophic food webs. These data describe the feeding volume (non-negative) among organisms grouped into nodes, called trophic species, that form the food web. Model complexity arises due to the extensive amount of zeros in the data, as each node in the web is predator/prey to only a small number of other trophic species. Many of the zeros are regarded as structural (non-random) in the context of feeding behavior. The presence of basal prey and top predator nodes (those who never consume and those who are never consumed, with probability 1) creates additional complexity to the statistical modeling. We develop a special statistical social network model to account for such network features. The model is applied to two empirical food webs; focus is on the web for which the population size of seals is of concern to various commercial fisheries.     

Robust estimation of a multilevel model with structural change

We postulate a spatiotemporal multilevel model and estimate using forward search algorithm and MLE imbedded into the backfitting algorithm. Forward search algorithm ensures robustness of the estimates by filtering the effect of temporary structural changes in the estimation of the group-level covariates, the individual-level covariates and spatial parameters. Backfitting algorithm provides computational efficiency of estimation procedure assuming an additive model. Simulation studies show that estimates are robust even in the presence of structural changes induced for example by epidemic outbreak. The model also produced robust estimates even for small sample and short time series common in epidemiological settings.     

双模网络下基于节点流行度的潜在空间模型

本文提出了双模网络下基于节点流行度的潜在空间模型，不仅能够显式地表达节点间产生连接的概率，而且可以推导出双模网络的连接的传递性、节点度的异质性等特征，这些特征可以通过数值化定量的方式描述网络生成过程中的常见规律。在此基础之上，本文进一步提出了加权概率指标，用以衡量双模网络的节点间未来产生连接的可能性。最后，本文分别在模拟数据、公开数据集和某在线点评网站的商户一消费者网络数据上验证了模型假设符合实际数据的分布，并使用加权概率指标与其他多种双模网络链路预测的方法进行比较分析。实验结果表明，本文提出的方法不仅可以量化分析网络生成过程中的特征，而且在实验数据上的链路预测能力整体优于其他双模链路预测方法。     

Time series modelling of childhood diseases: a dynamical systems approach

A key issue in the dynamical modelling of epidemics is the synthesis of complex mathematical models and data by means of time series analysis. We report such an approach, focusing on the particularly well-documented case of measles. We propose the use of a discrete time epidemic model comprising the infected and susceptible class as state variables. The model uses a discrete time version of the susceptible–exposed–infected–recovered type epidemic models, which can be fitted to observed disease incidence time series. We describe a method for reconstructing the dynamics of the susceptible class, which is an unobserved state variable of the dynamical system. The model provides a remarkable fit to the data on case reports of measles in England and Wales from 1944 to 1964. Morever, its systematic part explains the well-documented predominant biennial cyclic pattern. We study the dynamic behaviour of the time series model and show that episodes of annual cyclicity, which have not previously been explained quantitatively, arise as a response to a quicker replenishment of the susceptible class during the baby boom, around 1947.     

End-to-end queuing delay assessment in multi-service ip networks

Packet-based networks are more and more used to transport interactive streaming services like telephony and videophony. To guarantee a good quality for these services, the queuing delay and delay jitter introduced in the transport of voice or video flows over the packet-based network should be kept under control. Because data sources tend to increase their sending rate until (a part of) the network is congested, mixing real-time traffic and data traffic in one queue would lead to unacceptable high delays for real-time services. Therefore, voice and video packets need to get preferential treatment ( e.g. head-of-line priority) over data packets in the network nodes. Therefore, the queuing behavior of the voice and video packets can be studied more or less independently from the traffic generated by data services. Simple methods to assess the end-to-end delay are primordial. Since it is well known that an aggregate of voice (and CBR video) sources is accurately modeled by a Poisson arrival process and that delays in consecutive nodes are more or less statistically independent, this boils down to developing methods to calculate quantiles of the total queuing delay through a system of N statistically independent M/G/1 nodes. This paper develops four methods to calculate quantiles of the total queuing delay: a Gaussian method, a method based on the numerical inversion of the moment generating function of the total queuing delay developed by Abate and Whitt and two methods based on the assumption that the tail distribution of the individual queuing delay of one node is approximately exponential. The Gaussian method is the simplest, but only gives crude results. The method of Abate and Whitt is the most complex and breaks down for large quantiles. The methods based on the assumption of an exponential tail produce results that are more or less equally accurate as long as there is a node where the load is high enough.     

Statistical analysis of controlled calibration model with replicates

In this work, we generalize the controlled calibration model by assuming replication on both variables. Likelihood-based methodology is used to estimate the model parameters and the Fisher information matrix is used to construct confidence intervals for the unknown value of the regressor variable. Further, we study the local influence diagnostic method which is based on the conditional expectation of the complete-data log-likelihood function related to the EM algorithm. Some useful perturbation schemes are discussed. A simulation study is carried out to assess the effect of the measurement error on the estimation of the parameter of interest. This new approach is illustrated with a real data set.     

A random effects model for diseases with heterogeneous rates of infection

One form of data collected in the study of infectious diseases is on the transmission of a disease within households. We consider a model which allows the rate of disease transmission to vary between households. A Bayesian hierarchical approach to fitting the model is proposed and is implemented by the Metropolis–Hastings algorithm, a standard Markov chain Monte Carlo (MCMC) method. Results are presented for both simulated epidemic chain data and the Providence measles data, illustrating the potential that MCMC methods have to dealing with heterogeneity in infectious disease transmission.